problem using option fleqn in amsmath package

Set the length \mathindent to zero:

\setlength{\mathindent}{0pt}

EDIT: you can regulate that distance by setting \mathindent (to 0pt, for example), with a \setlength\mathindent{<value>}

\documentclass[fleqn]{article}

\usepackage{amsmath}
\setlength\parindent{0pt}

\begin{document}
\hrulefill

\begin{align}
a_1 &= b_1+c_1\\
a_2 &= b_2+c_2-d_2+e_2
\end{align}

\setlength\mathindent{0pt}
\hrulefill

\begin{align}
a_1 &= b_1+c_1\\
a_2 &= b_2+c_2-d_2+e_2
\end{align}

\end{document}

Using Thorsten's method affects the math indent for the whole page. If that's not what you want I would suggest using the nccmath package for fleqn like this:

\documentclass{article}
\usepackage{nccmath}
\begin{document}
\noindent This is text on the page here.\\
\begin{fleqn}[0pt]
\begin{align*}
a_1 &= b_1+c_1 \\
a_2 &= b_2+c_2-d_2+e_2\\
\end{align*}
\end{fleqn}
This is more text on the page down here.\\
\end{document}